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Barycentric Simplicial Hashing (BSH) 🔺
A Four-State Topological Hash Competitive with Industry-Standard Product Quantization at Half the Memory.
Author: Andres Sebastian Pirolo
ORCID: 0009-0004-3899-1222
Email: lctrnc1@gmail.com
DOI: [insert after Zenodo upload]
🚀 The Breakthrough
Barycentric Simplicial Hashing (BSH) is a hardware and software-agnostic mathematical framework that uses the local triangulation of a vector space as a discrete coordinate system for Approximate Nearest Neighbor (ANN) search.
By extending the natural three-vertex zone assignment with a fourth state (the triangle barycentre), BSH creates a topological buffer zone. This turns the curse of dimensionality into a feature, assigning >51% of vectors to the barycentre region in 24D spaces.
📊 Core Benchmark (Out-of-Sample)
| Method | Recall@1 (OOS) | Memory Footprint | Lift over Random |
|---|---|---|---|
| 3-state Hash | 64.5% | 34 bytes | 14.3x |
| BSH 4-state (This Work) | 84–90% | 34–57 bytes | 18.7x |
| FAISS IVF-PQ | 85–90% | 64 bytes | — |
Tested on completely independent distributions (never seen during index construction) using ARM Cortex-X3.
🔒 Intellectual Property & Commercial Licensing
This repository contains the official research paper outlining the mathematical algorithms and pseudocode for BSH.
The theoretical framework is published as Prior Art to prevent third-party patenting of simplicial complex indexing, four-state barycentric quantization, and related RAG/LLM applications.
Proprietary Implementation Available
The highly optimized, production-ready C++ / ARM NEON SIMD implementation is retained as a Trade Secret. It is exceptionally fast, avoiding full matrix instantiations via implicit L1 Laplacian power iterations and barycentric popcount hashing.
Strategic Commercial Licensing & First-Mover Advantage: Entities seeking to integrate BSH into production LLM inference, vector databases, or on-device AI accelerators should secure licensing rights.
For commercial licensing of the intellectual property or the proprietary C++ engine, contact: lctrnc1@gmail.com
📄 License
- Paper: CC BY-NC-ND 4.0
- Commercial Application of the Math/Algorithms: Requires explicit written authorization. See
LICENSE.mdfor full Layer-3 Commercial Notice.